We report the superconductivity in Ca-intercalated bilayer graphene C$_6$CaC$_6$, the thinnest limit of Ca graphite intercalation compound. We performed textit{in situ} electrical transport measurements on pristine bilayer graphene, C$_6$LiC$_6$ and C$_6$CaC$_6$ fabricated on SiC substrate under zero and non-zero magnetic field. While both bilayer graphene and C$_6$LiC$_6$ show non-superconducting behavior, C$_6$CaC$_6$ exhibits the superconductivity with transition temperature ($T_{{rm c}}$) of 4.0 K. The observed $T_{{rm c}}$ in C$_6$CaC$_6$ and the absence of superconductivity in C$_6$LiC$_6$ show a good agreement with the theoretical prediction, suggesting the importance of a free-electron-like metallic band at the Fermi level to drive the superconductivity.
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